Question 1042956
Statement is true.


x and y are rational by definition, so let c equal the least common denominator of x and y. Then you can find a and b such that x = a/c and y = b/c.


Formally, let *[tex \large x = \frac{p}{q}] and *[tex \large y = \frac{r}{s}] where p, q, r, s are integers, *[tex \large q, s > 0] and *[tex \large gcd(p,q) = 1], *[tex \large gcd(r,s) = 1] (i.e. fractions in simplest form). Then *[tex \large c = gcd(q,s)], *[tex \large a = \frac{p \cdot gcd(q,s)}{q}] and *[tex \large b = \frac{r \cdot gcd(q,s)}{s}] is an example set of values.